We considered a fairly simple model for the growth of two species (or groups) of algae, in the form of a non-autonomous dynamical system. The only variable parameter in this model is the effect of light intensity on growth. Using a simple averaging procedure, we obtained a system which approximately describes the variation of the daily average concentration of living and dead algae. A stability analysis of the equilibria of this system is given, and it is shown that several bifurcation sequences are possible, depending on the properties of the algae. Knowledge of these sequences is helpful when predicting algal blooms.